[Solved] Remarks in equations with arrows

Mathy Asks: Remarks in equations with arrows
In huge calculations it’s often very helpful as reader to have nice remarks about which manipulation was made. Also, other remarks in equations can help alot, e.g., this one

enter image description here

which I like more than the ^-convention. I am generating the above with the following code

vertarrowbox{e_j}{$i$textsuperscript{th} spot}


    begin{array}[t]{@{}c@{}} #2 \[-0.7ex]
        leftuparrowvcenter{hrule height #1}right.kern-nulldelimiterspace\[-1.2ex]

My goal now is to achieve something similar. I am looking for something like this

enter image description here

to denote that the exchange of the two variables gives a minus sign.

I wonder how I could implement this. I am not sure if tikz-cd is the way to go (I don’t have experience with tikz-cd in equations like this and don’t know if it is even possible to use it this way).

Thank you for your ideas!

Ten-tools.com may not be responsible for the answers or solutions given to any question asked by the users. All Answers or responses are user generated answers and we do not have proof of its validity or correctness. Please vote for the answer that helped you in order to help others find out which is the most helpful answer. Questions labeled as solved may be solved or may not be solved depending on the type of question and the date posted for some posts may be scheduled to be deleted periodically. Do not hesitate to share your response here to help other visitors like you. Thank you, Ten-tools.